Least Common Multiple (LCM) of 99 and 106
The least common multiple (LCM) of 99 and 106 is 10494.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 99 and 106?
First, calculate the GCD of 99 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 106 = 0 remainder 99 |
| 2 | 106 ÷ 99 = 1 remainder 7 |
| 3 | 99 ÷ 7 = 14 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 31 | 124 |
| 46 and 149 | 6854 |
| 145 and 32 | 4640 |
| 101 and 97 | 9797 |
| 183 and 157 | 28731 |